The last result determines the minimum number of maximal independent sets in twin-free trees. This was previously proven by Taletskiĭ and Malyshev in [1]}. We give a shorter proof in Section , which starts by deriving the bounds, in contrast to [1]} where the extremal graphs are characterized first by excluding certain structures in the extremal graphs.
We use an inductive approach, based on a lemma of Wilf [3]}.
